The yrast states of nuclei that are spherical or weakly deformed in their ground states are described as quadrupole waves running over the nuclear surface, which we call "tidal waves". The energies and 142 transition probabilities of the yrast states in nuclides with Z=44, 46, 48 and N=56, 58, ... , 66 are calculated by means of the cranking model in a microscopic way. The nonlinear response of the nucleonic orbitals results in a strong coupling between shape and single particle degrees of freedom.